University of Warsaw, Warsaw, Poland; Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine
raeirina@imath.kiev.ua, raemarina@imath.kiev.ua
The classification of all nearrings up to certain orders is an open problem. It requires extensive computations, and the most suitable platform for their implementation is the computational algebra system GAP [1].
Until well into 1990th the interest of pure mathematicians in nearring theory was stirred by, but in most cases also confined to the information that was produced by theoretical results for some research problems. However 28 years ago the developers of the GAP package SONATA [2] shown the implementation of nearring theoretical algorithms. These are gradually becoming accepted both as standard tools for a working nearring theoretician, like certain methods of proof, and as worthwhile objects of study, like connections between notions expressed in theorems. The SONATA package provides methods for the construction and analysis of finite nearrings, as well as the library of all nearrings up to order 15 and all nearrings with identity up to order 31.
The current version of the LocalNR package [3] (not yet redistributed with GAP) contains the library of local nearrings of order at most 361 (except those of orders 32, 64, 128, 243 and 256) and some functions to analyze finite nearrings. We have already calculated some classes of local nearrings of orders 32, 64, 128, 243 and 625 (see, for example, [4-7]).
Acknowledgements. Authors would like to thank to IIE-SRF for supporting of their fellowships at the University of Warsaw.
The GAP Group, GAP — Groups, Algorithms, and Programming, Version 4.12.0; 2022, https://www.gap-system.org
Aichinger E., Binder F., Ecker Ju., Mayr P. and Noebauer C. SONATA — system of near-rings and their applications, GAP package, Version 2.9.1, 2018, https://gap-packages.github.io/sonata/
Raievska I., Raievska M., Sysak Y. LocalNR, Package of local nearrings, Version 1.0.3 (2021) (GAP package), https://gap-packages.github.io/LocalNR
Raievska I., Raievska M., Sysak Ya. (2023). DatabaseEndom625: (v0.2) [Data set]. Zenodo, https://zenodo.org/record/7613145#.ZChqJXZBy39
Raievska I., Raievska M., Sysak Ya. (2022). DatabaseEndom128: (v0.2) [Data set]. Zenodo, https://zenodo.org/record/7225377#.Y7blWYfMKM8
Raievska I., Raievska M. Groups of nilpotency class 2 of order $p^4$ as additive groups of local nearrings. 2023, https://arxiv.org/abs/2303.17567
Raievska I., Raievska M. Groups of nilpotency class 3 of order $p^4$ as additive groups of local nearrings. 2023, https://arxiv.org/abs/2309.14342